Space Flight
Interplanetary Transfers
History
Pioneers
• Konstantin Tsiokovsky
• Robert Goddard
• Hermann Oberth
Overview
• Space Flight
• Trajectories with Chemical Rockets
• Interplanetary Superhighway
• Hoffman Transfers
• Gravitational ‘Slingshot’
• Space Vehicles of future
• Conclusions
Thrust
• Thrust is a reaction force described
quantitatively by Newton's Second Law
when a system expels or accelerates
mass in one direction to propel a vehicle in
the opposite direction
• d(mv)/dt = v(dm/dt) + m(dv/dt)
Delta-V
• Delta-v is a measure used in
astrodynamics to describe the amount of
"effort" needed to carry out an orbital
maneuver ; to change from one orbit to
another
Gravitational Sphere of influence
• Laplace derived the following for the Radius of
the Sphere of Influence
• rP = DSP [MP/MSun]2/5
Where
• DSP = the distance between the Sun and the
Planet
• MP = mass of the planet
• MSun= mass of the Sun
Example: Jupiter and Earth
• Jupiter:
MSun/MJ = 1047
DSP =5.02 AU
rJ = 48.3 million km = 657 RJupiter
• Earth:
MSun/Mearth = 333,000
DSP = 1 AU
re = 927,000 km
= 2.4 x distance from Earth to the Moon
= 145 Rearth
• What is the most
important thing for a
Space Travel Project
• For a SSTO, fuel and fuel tank constitutes
88% of the total launch weight and 67%
for a single stage rocket
• Lowering the delta-v requirements is one
of the most important considerations as it
implies less thrust is needed which in turn
means less fuel and more payload
Least energy transfers
• Launch site and direction of launch
• Interplanetary Superhighway
• Hoffman Energy Transfers
• Gravitational Slingshot
Launch site
• Launch from near equator
Sitting on the launch pad near the equator,
a rocket is already moving at a speed of
over 0.4 km per second relative to Earth's
center.
Direction of Launch
• Outward Bound :
Launch in the direction of Earth’s rotation
around its own axis (towards east) and
launch towards the rotation around the sun
(average velocity of approximately 29
km/sec along its orbital path)
http://www2.jpl.nasa.gov/basics/bsf14-1.html
Inward Bound : Do the opposite
Interplanetary Superhighways
• Lowest Delta-V requirements
• based around a series of orbital paths
leading to and from the unstable orbits
around the Lagrange points
Hohmann Transfer
• First proposed in 1925 by German
scientist Walter Hohmann
• Most useful for launch to Mars and Venus
• Space craft are launched to have an
elliptical orbit .
• The space craft covers less than 180
degrees in its orbit around the sun before
reaching its target( Type I trajectory)
• For superior planets perihelion is at earth
and aphelion is at the planet. Energy
increased at perihelion to increase
aphelion distance
• For inferior planets aphelion is at earth
and perihelion is at the planet. Energy
decreased at aphelion to decrease
perihelion distance
Travel to Mars
The spacecraft is already in solar orbit as it
sits on the launch pad. This existing solar
orbit must be adjusted to cause it to take
the spacecraft to Mars: The desired orbit's
perihelion (closest approach to the sun)
will be at the distance of Earth's orbit, and
the aphelion (farthest distance from the
sun) will be at the distance of Mars' orbit
• perihelion= Earth orbital radius = 1 AU
• aphelion= Mars orbital radius = 1.524 AU
• semimajor axis ‘a’ of probe orbit
a = (perihelion+ aphelion)/2= 1.262 AU
• Using Kepler's third law to determine the
orbital period, P.
P2 = a3
period = (1.262)3/2 = 1.418 years = 518
days
• Since the probe takes half of a period to
get to Mars, the time of flight is 259 days
or 0.709 years.
Launch Window
• This means that the probe must be
launched 259 days before Mars is at its
position in its orbit where the probe will
intercept Mars. Mars' orbital period is 1.88
years and it will move 136 degrees in its
orbit during the probe's trip to Mars.
• Therefore at the time of launch Mars must
be (180-136)=44 degrees greater
heliocentric longitude than the Earth
Delta-V
Using Kepler's second law calculate delta-v.
• The relative velocities are inversely
proportion to the respective distances from
the sun.
rperihelion*vperihelion = raphelion*vaphelion
• vperihelion = vcircular[(1+e)/(1-e)]1/2
• vaphelion = vcircular[(1-e)/(1-e)]1/2
• The circular velocity is the average
velocity in orbit = 2πa/P
Circular velocity = 26.5 km/sec
vperihelion = 32.7 km/s
• The Earth is moving at 29.7 km/s in its
orbit, the velocity of the probe must be
increased by 3.0 km/s relative to the Earth.
• This ignores the pull of the Earth's gravity
and is true when the probe is outside the
influence of Earth's gravity
• Similarly the vaphelion is 30km/sec, so the
probe has to be slowed by 2.7km/sec to
make it orbit around Mars
Gravitational Slingshot
• First suggested by Italian born American
Scientist Giuseppe 'Bepi' Colombo
• The probe ‘steals’ some of the angular
momentum from a planet to increase its
own speed, this barely has any impact on
the planets velocity.
• If spacecraft passes behind the motion of
the planet craft gains speed and loses
speed if it passes in from.
• Escape velocity from earth is about 11.2 km/sec
• If we manage to hurl a spacecraft at this speed
from the ground then it escapes from the earth’s
orbit.
• It will still be in an identical earth like orbit
around the sun
• Escape velocity from solar system at earth’s
orbit is 43km/sec
• To send it to an outer planet or even out of the
solar system we need to give the spacecraft
enough energy
Assist from Jupiter
• First the space probe is sent to Jupiter
using a Hohmann transfer
• The delta-v needed just out of earth’s
(perihelion) sphere of influence is 10.15
km/sec(39.95-29.8) (heliocentric
velocities)
• The craft loses energy steadily as it tries to
climb out of the potential well.
• On arrival at Jupiter (aphelion) the speed
of the aircraft is 9.36 km/sec
• The craft enters
Jupiter’s sphere of
influence with a
velocity greater than
the escape velocity of
Jupiter (has to)
• It is attracted towards
Jupiter and the aircraft
gains speed as it
approaches the planet
Paradox
• The craft enters Jupiter’s sphere of influence
with a velocity greater than the escape velocity
of Jupiter (has to)
• It is attracted towards Jupiter and the aircraft
gains speed as it approaches the planet
• After the point of closest approach the craft has
maximum velocity and it starts to lose velocity.
• Effectively it leaves Jupiter’s sphere of influence
at the same speed at which it enters.
• So where did the gain in velocity come
from ?
• The important thing to notice here is we
need to increase the velocity of the
spacecraft in the heliocentric frame
• Skipping some the vector math, consider
conservation of linear momentum
mΔv=MΔV
• The v,V are in heliocentric frame of
reference. So the gain in velocity of the
spacecraft happens only if the planet itself
is moving with respect to the sun.
• ΔV is of the order of 10-25
• We could make the spacecraft fly
repeatedly around the planets if we can
find a perfect launch window and attain
huge speeds.
• But the faster the spacecraft flies the
harder it is for any planet to influence it
with its gravity.
• If we ever found a star system consisting
of multiple black holes orbiting each other,
we might be able to apply this scheme to
achieve relativistic speeds, by looping
around from one to the other. I suppose in
this situation the achievable speed limit
would depend on how close a spaceship
could pass without be being destroyed by
tidal forces. Still, if the black holes were
large enough, the tidal forces even at the
event horizon would be tolerable. Also,
stopping at our destination might be tricky.
Some Examples
• Messenger is expected to reach Mercury
by 2011
• It will fly once past Earth, twice past Venus
and three times past Mercury for gravity
assists — and make 15 loops around the
sun — before slowing enough to slip into
orbit around Mercury
Voyager 2
Cassini and Ulysses
• http://www.esa.int/esaCP/SEMXLE0P4HD_index_0.html
Limits on Chemical Rockets
• Achieving higher speeds require more
fuel, which means added weight , which in
turn makes it hard to increase a rockets
speed
• Even for small robotic missions the
theoretical limit for chemical rockets is
.001c
• Interstellar travel ruled out
Future space Vehicles
• Nuclear Propulsion
• Project Orion
• Project Daedalus
• Project Prometheus
• Matter-Antimatter Engines
• Solar Sails and beamed energy propulsion
• Interstellar Ramjets
Nuclear Propulsion
• Project Orion
• Lasted from 1958 to 1965
• Envisaged exploding nuclear bombs a few tenths
of meters behind the rocket
• Vaporized debris would impact a pusher plate on
the back of spacecraft
• Could be build from existing technology but would
violate international agreements banning nuclear
explosions in space
Project Daedalus
• British conceived
project
• Relies on continuos
stream of energy
from on board
controlled fusion
reaction
• Out of current
technological limits
• Can achieve 0.01c
like project Orion
Project Prometheus
• Spacecraft called Jupiter Moons icy orbiter
• Work on this is currently going on
• Will use electric propulsion from a small
fission reactor
Matter-Antimatter Engines
• Theoretically can provide the most power
per unit weight of fuel
• Can reach 90% speed of light
• To create 1 kg of anitmatter today requires
more than annual fuel requirements of the
world
• Problem of containing antimatter
• Out of current technology limits
Sails and Beamed Energy
• Already tried
• Will have large, lightweight sails to be
powered by radiation pressure from sun
for small but continuous acceleration
• After sun’s radiation becomes weak,
powerful lasers can be shone at the sails
• Not possible to build such a laser today
• There is a problem of trying to stop .
Sails and Beamed Energy
Interstellar Ramjets
• Collects interstellar hydrogen for fuel with
a giant scoop.
• Can reach very close to speed of light
because it can accelerate continuosly
• Slowing down will not be a problem
• Still needs controlled fusion reaction and
hence out of bounds of current technology
Interstellar Ramjets
References
•
Books
•
•
•
•
Elements of Space Technology-Rudolf Meyer
Rockets into space-Frank Winter
The Cosmic Perspective- Jeffrey Bennett, Megan
Donahue, Nicholas Donahue, Mark Voit
Classical Dynamics-Marion and Thornton
• Websites
• http://encyclopedia.thefreedictionary.com/Gravitational%20sli
ngshot
• http://www.mathpages.com/home/kmath114.htm
• http://www.go.ednet.ns.ca/~larry/orbits/gravasst/gravasst.htm
l
• http://saturn.jpl.nasa.gov/mission/gravity-assist-primer.cfm
• http://en.wikipedia.org/wiki/Gravitational_slingshot
• http://www.esa.int/esaCP/SEMXLE0P4HD_index_0.html